Survival analysis and estimating functions

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This proposal deals with statistical methods appropriate to model and predict real physical phenomena subject to appreciable random variation. Areas of application include engineering reliability, medical statistics and geostatistics. For example, in medical statistics, models for clinical trial data which include estimation of cure rates for diseases such as cancer are considered. I develop a variety of novel cure rate models by modeling the underlying health status of individuals as a stochastic (random) process. When this process reaches a critical threshold failure ensues. If there is a positive probability that the threshold is not attained, then there exist immune or cured individuals in the population. Estimating cure proportions and assessing the impact of various covariates on the proportion cured is of great scientific significance. Similar models are also very useful in engineering reliability where some cumulative damage process results in failure when a critical threshold is attained. These threshold models are an exciting alternative to models such as the well-studied Cox model, frequently used in medical statistics, or the accelerated failure time model which is popular in engineering reliability. There is great scope for new methodological development and applications of these new models to real scientific and technological problems. This is a very exciting alternative paradigm to more conventional modeling approaches.